I believe that the only way the US could legally do that is by exerting control over up/downlink stations that are in US jurisdiction. I'm assuming that things like Starlink will have up and downlink stations in places outside of the US as well as inside.

Extralegally, though? All bets are off.

SpaceX is a US corporation, therefore US jurisdiction.

You're making an assumption that Starlink will fight a nudge by the US government instead of quietly complying.

I'm not, really. That's why I added my "all bets are off" comment.

I can't see every other nation being too happy about US-controlled global Internet service. They will demand some degree of control over their territories. I can see the space law getting some updates sometime soon.